A. M. Elsawah (Ahmed Elsawah)
Ahmed Elsawah works at
1- Department of Statistics and Data Science, Faculty of Science and Technology, Beijing Normal University-Hong Kong Baptist University United International College.
2- Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science.
3- Department of Mathematics, Faculty of Science, Zagazig University.
The current research work are supported by (Elsawah greatly appreciates their kind support)
1- UIC Research Grants with No. of (R201810 ).
2- UIC Research Grants with No. of (R201912 ).
3- UIC Research Grants with No. of (R202010).
4- Curriculum Development and Teaching Enhancement with No. of (UICR0400046-21CTL).
5- Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science with No. of (2022B1212010006).
6- Guangdong Higher Education Upgrading Plan (2021–2025), China with No. of (UIC R0400001-22).
1- Department of Statistics and Data Science, Faculty of Science and Technology, Beijing Normal University-Hong Kong Baptist University United International College.
2- Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science.
3- Department of Mathematics, Faculty of Science, Zagazig University.
The current research work are supported by (Elsawah greatly appreciates their kind support)
1- UIC Research Grants with No. of (R201810 ).
2- UIC Research Grants with No. of (R201912 ).
3- UIC Research Grants with No. of (R202010).
4- Curriculum Development and Teaching Enhancement with No. of (UICR0400046-21CTL).
5- Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science with No. of (2022B1212010006).
6- Guangdong Higher Education Upgrading Plan (2021–2025), China with No. of (UIC R0400001-22).
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Papers by A. M. Elsawah (Ahmed Elsawah)
The outline of the thesis is as follows:-
Chapter one : In this Chapter, we simply give an elementary introduction to
ordered random variables (rv’s) and gos, which should be regarded as a bare essential
description on the topic that would facilitate the reader to follow the subseqent
chapters of this thesis. The asymptotic theory of extreme oos, record values and
gos and their duals are discussed. The asymptotic behavior of functions of oos, e.g.,
quasi-range, quasi-midrange, extremal quotient and extremal product is presented.
Finally, we study the relationship between the normalizing constants and the sample
size for order statistics, gos and its dual.
Chapter two : In this chapter necessary and sufficient conditions are obtained for
the weak convergence of the generalized and dual generalized range and mid range
when m > −1, and for the record values for the case m = −1. The class of possible
non-degenerate limit df’s of the above statistics is characterized.
Chapter three : In this chapter necessary and sufficient conditions are obtained
for the weak convergence of the generalized and the dual generalized extremal product
when m > −1 and for the record values for the case m = −1. The class of
possible non-degenerate limit dfs of the above statistics is characterized.
Chapter four : In this chapter necessary and sufficient conditions are obtained
for the weak convergence of the generalized and the dual generalized extremal quotient
when m > −1, and for the record values for the case m = −1. The class of
possible non-degenerate limit dfs of the above statistics is characterized.
Chapter ve : This chapter deals with some applications and comparisons between
the statistics which are studied throughout the preceding chapters. The
asymptotic behavior of the generalized symmetric difference is connected with the
asymptotic behavior of the generalized range and generalized extremal quotient. In
this chapter the generalized symmetric difference is studied as an application of the
study on the generalized range and generalized extremal quotient. Finally, several
examples for the most important distribution functions are given.
It is worth mentioning that most of the results obtained in this thesis have been
published or submitted for publication.